My sixth grade math classroom has a curriculum that is heavily literacy based. Students must read through real world word problems and figure out the math through exploration. The lesson I chose out of the Connected Mathematics Covering and Surrounding’s book is titled, “Designing Bumper-Car Rides” (Lappan, Fey, Fitzgerald, Friel, & Phillips, 2004). The lesson’s content objective is that students will use their knowledge of area and perimeter by applying it to the creating of bumper-car rides. Students need to “learn that the area of an object is the number of unit squares needed to cover it and the perimeter of an object is the number of units of length needed to surround it” (Lappan, Fey, Fitzgerald, Friel, & Phillips, 2004).
This lesson is relevant in the real world, because students may need this knowledge and skill set to create designs of buildings, parks, houses, etc. one day. First I will read aloud a short piece of text that will get students engaged as it describes the company who creates rides at amusements parks and how mathematical thinking is used to create these scream makers. I will explain that students may one day want to design something unique of their own, so they need the mathematical skills to do this. The lesson will be introduced, explaining the problem “When MARs gets an order for a bumper-car ride, their designers sometimes use square tiles to model the possible floor plans, and then send sketches of their ideas to the customer for approval” (Lappan, Fey, Fitzgerald, Friel, & Phillips, 2004, p. 7). I will tell the students that they are the designers that will be creating designs which will be submitted to their customer for approval. Students will be challenged to come up with the best design. Because I have a diverse group of students, I will allow students to choose which learning environment best suits their learning style. They will have the choice of working independently or in pairs for this design process. The task will be presented as “Badger State Shows in Wisconsin requested a bumper-car ride with a total of 36 square meters of floor space and 26 rail sections. Sketch some possible designs for this floor plan” (Lappan, Fey, Fitzgerald, Friel, & Phillips, 2004, p. 7). Students will use one inch grid paper to begin drawing their designs. When students are running out of ideas, I will bring out the square tile manipulatives. Students who are better with visually seeing the tiles and manipulating them kinesthetically will also benefit greatly from this modification. As students think their options are again exhausted, I will have individuals and pairs go to the website http://www.shodor.org/interactivate/activities/AreaExplorer/. At this site, students can put in the perimeter needed for the design, and the program will create a design. Students must then check the design to make sure it has 36 square tiles for area if they want to use the design given. Additional designs can be sketched on the grid paper as students find more design options. I will walk around to monitor student progress, making sure there are 36 square tiles covering the design, and 26 rail sections surrounding the design.
When the groups are finished with possible design options, they must choose individually which design is best. At this time, I will begin the assessment process. Students will log on to the math class blog, and they will write to persuade. Their job is to persuade Badger State Shows to pick their design by describing the design and the reason it is superior to any other. In their blog paragraph, they must include the vocabulary words area, perimeter, covering, surrounding, floor space, rail sections, titles, and square tiles.
References:
Lappan, G., Fey, J., Fitzgerlad, W., Friel, S., and Phillips, E. (2004). Connected mathematics: Data about us. Glenview, IL: Pearson Prentice Hall.
Online Social Networking Lesson
In the 6th grade Connected Math unit Measuring Area and Perimeter, the students were asked in the first PBL lesson to create bumper car designs with a specific area and perimeter (Lappan, Fey, Fitzgerald, Friel, & Phillips, 2004). To get students on topic, I will give background knowledge of the previous lesson. Students will log on to the math class blog, and they will write to persuade. Their job is to persuade Badger State Shows to pick their favorite design created yesterday by describing the design and the reason it is superior to any other. In their blog paragraph, they must include the vocabulary words area, perimeter, covering, surrounding, floor space, rail sections, titles, and square tiles. When students are asked to write out their content knowledge on a blog, they are learning how to communicate online. Learning in the 21st century should have a “community of learners where students can explore mathematical topics in depth and connect those topics to real-life situations” (Cennamo, Ross, and Ertmer, 2009, p. 256).
The next lesson in the unit is called Decoding Designs where several designs are given, and students have to figure out the area and perimeter of each design (Lappan, Fey, Fitzgerald, Friel, & Phillips, 2004). The students are given three bumper car floor plan designs. The content objective is for the students to figure out “which of the three designs provides the greatest floor space (has the greatest area)…[and] which of the three designs requires the most rail sections (has the greatest perimeter” (Lappan, Fey, Fitzgerald, Friel, & Phillips, 2004, p. 9). Because the sample floor tile sections are one inch by one inch, the same as a Cheese It cracker, I will have students use Cheese Its as their manipulatives. I have included this modification for those students who need hands-on, kinesthetic activities to learn. Students are always more engaged when using food items, and it is fun to eat the manipulatives after the lesson. I will of course need to make sure the ingredients in Cheese Its are okay for all religious backgrounds and that non of my students are allergic to the ingredients. In order to manage this lesson, I will have individual Ziplock bags already prepared with enough Cheese Its to cover the largest design area.
In groups, students will work together using their Cheese It crackers to find the area and perimeter of the three designs. After groups have explored by labeling each design with the area and perimeter, we would reflect on the learning. I have the class do this reflection activity, because “when we stop to think about what we [they] have learned and to reflect on how we [they] learned it, we [they] actually achieve a deeper understanding of the knowledge we have constructed” (Cennamo, Ross, and Ertmer, 2009, p. 33). As a whole group, individual students would share strategies for finding area. Some students may talk about multiplying base times height, whereas others may discuss placing a Cheese It cracker down one by one until the whole design space was filled. In their math journals, students would answer the content objectives.
To enrich this activity further, we would login to the blog once again to use social networking in the classroom. Students would answer to the blog prompt “Choose the design you think is best, and explain how you would sell it to a customer” ” (Lappan, Fey, Fitzgerald, Friel, & Phillips, 2004, p. 9). I would again have students use the vocabulary words area, perimeter, covering, surrounding, floor space, rail sections, titles, and square tiles. I believe the “use of technology in mathematics learning… give students opportunities to develop ideas and skills in an environment that promotes creative thinking” (Cennamo, Ross, and Ertmer, 2009, p. 252). Students are asked to think beyond the activity and apply their knowledge to the real world, furthering the problem based learning. According to Cennamo, Ross, and Ertmer (2009), “creativity is often developed through an authentic instructional approach…[where students] appy their creativity to solve authentic problems” (p.27). Students will really have to think about the floor space, the amount of rail sections, and which design would be best for the customer buying the bumper car design. The following day, students will comment on other classmate’s writing from this lesson or the previous lesson. I will assess students ability to discuss the mathematical reasoning about area and perimeter from their online communication. From their two initial posts and their comments to classmates, I will be able to see whether their knowledge is advanced, proficient, partially proficient, or unsatisfactory.
References:
Cennamo, K., Ross, J. & Ertmer, P. (2009). Technology Integration for Meaningful Classroom Use: A Standards-Based Approach. (Laureate Education, Inc., Custom ed.). Belmont, CA: Wadsworth, Cengage Learning. Lappan, G., Fey, J., Fitzgerlad, W., Friel, S., and Phillips, E. (2004). Connected mathematics: Data about us. Glenview, IL: Pearson Prentice Hall.
My sixth grade math classroom has a curriculum that is heavily literacy based. Students must read through real world word problems and figure out the math through exploration. The lesson I chose out of the Connected Mathematics Covering and Surrounding’s book is titled, “Designing Bumper-Car Rides” (Lappan, Fey, Fitzgerald, Friel, & Phillips, 2004). The lesson’s content objective is that students will use their knowledge of area and perimeter by applying it to the creating of bumper-car rides. Students need to “learn that the area of an object is the number of unit squares needed to cover it and the perimeter of an object is the number of units of length needed to surround it” (Lappan, Fey, Fitzgerald, Friel, & Phillips, 2004).
This lesson is relevant in the real world, because students may need this knowledge and skill set to create designs of buildings, parks, houses, etc. one day. First I will read aloud a short piece of text that will get students engaged as it describes the company who creates rides at amusements parks and how mathematical thinking is used to create these scream makers. I will explain that students may one day want to design something unique of their own, so they need the mathematical skills to do this. The lesson will be introduced, explaining the problem “When MARs gets an order for a bumper-car ride, their designers sometimes use square tiles to model the possible floor plans, and then send sketches of their ideas to the customer for approval” (Lappan, Fey, Fitzgerald, Friel, & Phillips, 2004, p. 7). I will tell the students that they are the designers that will be creating designs which will be submitted to their customer for approval. Students will be challenged to come up with the best design. Because I have a diverse group of students, I will allow students to choose which learning environment best suits their learning style. They will have the choice of working independently or in pairs for this design process. The task will be presented as “Badger State Shows in Wisconsin requested a bumper-car ride with a total of 36 square meters of floor space and 26 rail sections. Sketch some possible designs for this floor plan” (Lappan, Fey, Fitzgerald, Friel, & Phillips, 2004, p. 7). Students will use one inch grid paper to begin drawing their designs. When students are running out of ideas, I will bring out the square tile manipulatives. Students who are better with visually seeing the tiles and manipulating them kinesthetically will also benefit greatly from this modification. As students think their options are again exhausted, I will have individuals and pairs go to the website http://www.shodor.org/interactivate/activities/AreaExplorer/. At this site, students can put in the perimeter needed for the design, and the program will create a design. Students must then check the design to make sure it has 36 square tiles for area if they want to use the design given. Additional designs can be sketched on the grid paper as students find more design options. I will walk around to monitor student progress, making sure there are 36 square tiles covering the design, and 26 rail sections surrounding the design.
When the groups are finished with possible design options, they must choose individually which design is best. At this time, I will begin the assessment process. Students will log on to the math class blog, and they will write to persuade. Their job is to persuade Badger State Shows to pick their design by describing the design and the reason it is superior to any other. In their blog paragraph, they must include the vocabulary words area, perimeter, covering, surrounding, floor space, rail sections, titles, and square tiles.
References:
Lappan, G., Fey, J., Fitzgerlad, W., Friel, S., and Phillips, E. (2004). Connected mathematics: Data about us. Glenview, IL: Pearson Prentice Hall.
Online Social Networking Lesson
In the 6th grade Connected Math unit Measuring Area and Perimeter, the students were asked in the first PBL lesson to create bumper car designs with a specific area and perimeter (Lappan, Fey, Fitzgerald, Friel, & Phillips, 2004). To get students on topic, I will give background knowledge of the previous lesson. Students will log on to the math class blog, and they will write to persuade. Their job is to persuade Badger State Shows to pick their favorite design created yesterday by describing the design and the reason it is superior to any other. In their blog paragraph, they must include the vocabulary words area, perimeter, covering, surrounding, floor space, rail sections, titles, and square tiles. When students are asked to write out their content knowledge on a blog, they are learning how to communicate online. Learning in the 21st century should have a “community of learners where students can explore mathematical topics in depth and connect those topics to real-life situations” (Cennamo, Ross, and Ertmer, 2009, p. 256).The next lesson in the unit is called Decoding Designs where several designs are given, and students have to figure out the area and perimeter of each design (Lappan, Fey, Fitzgerald, Friel, & Phillips, 2004). The students are given three bumper car floor plan designs. The content objective is for the students to figure out “which of the three designs provides the greatest floor space (has the greatest area)…[and] which of the three designs requires the most rail sections (has the greatest perimeter” (Lappan, Fey, Fitzgerald, Friel, & Phillips, 2004, p. 9). Because the sample floor tile sections are one inch by one inch, the same as a Cheese It cracker, I will have students use Cheese Its as their manipulatives. I have included this modification for those students who need hands-on, kinesthetic activities to learn. Students are always more engaged when using food items, and it is fun to eat the manipulatives after the lesson. I will of course need to make sure the ingredients in Cheese Its are okay for all religious backgrounds and that non of my students are allergic to the ingredients. In order to manage this lesson, I will have individual Ziplock bags already prepared with enough Cheese Its to cover the largest design area.
In groups, students will work together using their Cheese It crackers to find the area and perimeter of the three designs. After groups have explored by labeling each design with the area and perimeter, we would reflect on the learning. I have the class do this reflection activity, because “when we stop to think about what we [they] have learned and to reflect on how we [they] learned it, we [they] actually achieve a deeper understanding of the knowledge we have constructed” (Cennamo, Ross, and Ertmer, 2009, p. 33). As a whole group, individual students would share strategies for finding area. Some students may talk about multiplying base times height, whereas others may discuss placing a Cheese It cracker down one by one until the whole design space was filled. In their math journals, students would answer the content objectives.
To enrich this activity further, we would login to the blog once again to use social networking in the classroom. Students would answer to the blog prompt “Choose the design you think is best, and explain how you would sell it to a customer” ” (Lappan, Fey, Fitzgerald, Friel, & Phillips, 2004, p. 9). I would again have students use the vocabulary words area, perimeter, covering, surrounding, floor space, rail sections, titles, and square tiles. I believe the “use of technology in mathematics learning… give students opportunities to develop ideas and skills in an environment that promotes creative thinking” (Cennamo, Ross, and Ertmer, 2009, p. 252). Students are asked to think beyond the activity and apply their knowledge to the real world, furthering the problem based learning. According to Cennamo, Ross, and Ertmer (2009), “creativity is often developed through an authentic instructional approach…[where students] appy their creativity to solve authentic problems” (p.27). Students will really have to think about the floor space, the amount of rail sections, and which design would be best for the customer buying the bumper car design. The following day, students will comment on other classmate’s writing from this lesson or the previous lesson. I will assess students ability to discuss the mathematical reasoning about area and perimeter from their online communication. From their two initial posts and their comments to classmates, I will be able to see whether their knowledge is advanced, proficient, partially proficient, or unsatisfactory.
References:
Cennamo, K., Ross, J. & Ertmer, P. (2009). Technology Integration for Meaningful Classroom Use: A Standards-Based Approach. (Laureate Education, Inc., Custom ed.). Belmont, CA: Wadsworth, Cengage Learning.
Lappan, G., Fey, J., Fitzgerlad, W., Friel, S., and Phillips, E. (2004). Connected mathematics: Data about us. Glenview, IL: Pearson Prentice Hall.